Signed Distance Function (SDF)-based volume rendering has demonstrated significant capabilities in surface reconstruction. Although promising, SDF-based methods often fail to capture detailed geometric structures, resulting in visible defects. By comparing SDF-based volume rendering to density-based volume rendering, we identify two main factors within the SDF-based approach that degrade surface quality: SDF-to-density representation and geometric regularization. These factors introduce challenges that hinder the optimization of the SDF field. To address these issues, we introduce NeuRodin, a novel two-stage neural surface reconstruction framework that not only achieves high-fidelity surface reconstruction but also retains the flexible optimization characteristics of density-based methods. NeuRodin incorporates innovative strategies that facilitate transformation of arbitrary topologies and reduce artifacts associated with density bias. Extensive evaluations on the Tanks and Temples and ScanNet++ datasets demonstrate the superiority of NeuRodin, showing strong reconstruction capabilities for both indoor and outdoor environments using solely posed RGB captures.